Call Libraries

library(tidyverse)
library(caret)
library(MASS)
library(car)
library(moments)

Calling the Transformed Datasets

income_cleaned = read_csv('NYS_Corp_Tax_Credit_data/income_cleaned.csv')
Rows: 1921 Columns: 6── Column specification ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (2): Name, Group
dbl (4): Year, Num, Amount, Avg
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
income_cleaned
industry_cleaned = read_csv('NYS_Corp_Tax_Credit_data/industry_cleaned.csv')
Rows: 2476 Columns: 6── Column specification ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (2): Name, Group
dbl (4): Year, Num, Amount, Avg
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
industry_cleaned

Creating the Models

sat.model.summary <- function (df, field, sat.formula){
    
    #Shapiro-Wilks test to evaluate normality
    print(shapiro.test(df[[field]]))
    
    #Kurtosis evaluation (normal distribution has a value close to 3)
    print('kurtosis')
    print(kurtosis(df[[field]]))
    linear.model.cleaned = lm(sat.formula, data = df)
    print(summary(linear.model.cleaned))
    plot(linear.model.cleaned)
    
    #histograms of response variable to check distribution
    print(df %>% 
      ggplot(aes_string(field)) + 
      geom_histogram() + 
      labs(title = 'Average Credit Amount Distribution') + 
      theme(plot.title = element_text(hjust = 0.5)))
    
    #Checking multicollinearity using VIF measurement
    print(vif(linear.model.cleaned))
    influencePlot(linear.model.cleaned)
    #avPlots(linear.model.cleaned)
}


sat.formula <- Avg ~ . - Amount
sat.field <- 'Avg'

sat.model.summary(income_cleaned, sat.field, sat.formula)

    Shapiro-Wilk normality test

data:  df[[field]]
W = 0.17297, p-value < 2.2e-16

[1] "kurtosis"
[1] 169.7518

Call:
lm(formula = sat.formula, data = df)

Residuals:
      Min        1Q    Median        3Q       Max 
-11338570   -547702     94139    421302  87181761 

Coefficients:
                                                                                                Estimate Std. Error t value Pr(>|t|)
(Intercept)                                                                                   -1.157e+08  5.512e+07  -2.100  0.03590
Year                                                                                           5.721e+04  2.731e+04   2.095  0.03634
NameAlternative Fuels and Electric Vehicle Recharging Property Credit                         -3.287e+05  1.242e+06  -0.265  0.79140
NameAlternative Minimum Tax Credit                                                             6.538e+05  9.757e+05   0.670  0.50286
NameBeer Production Credit                                                                     3.316e+05  1.290e+06   0.257  0.79715
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 6/23/08 but before 7/1/15  1.429e+06  9.960e+05   1.434  0.15162
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 7/1/15                     4.098e+06  1.421e+06   2.883  0.00398
NameBrownfield Tax Credits - Redevelopment Tax Credit - Prior to 6/23/08                       1.182e+06  9.927e+05   1.191  0.23386
NameBrownfield Tax Credits - Remediation Real Property Tax Credit                             -7.587e+04  9.920e+05  -0.076  0.93904
NameClean Heating Fuel Credit                                                                  7.148e+04  1.024e+06   0.070  0.94436
NameConservation Easement Tax Credit                                                           1.143e+05  1.064e+06   0.107  0.91444
NameCredit for Employment of Persons with Disabilities                                        -9.343e+05  1.119e+06  -0.835  0.40391
NameCredit for Purchase of an Automated External Defibrillator                                -1.449e+05  9.695e+05  -0.150  0.88117
NameCredit for Taxicabs & Livery Service Vehicles Accessible to Persons with Disabilities      2.316e+05  1.779e+06   0.130  0.89645
NameEmpire State Apprentice Tax Credit                                                        -7.983e+05  1.524e+06  -0.524  0.60040
NameEmpire State Commercial Production Credit                                                  2.183e+05  1.291e+06   0.169  0.86576
NameEmpire State Film Post Production Credit                                                   2.521e+04  1.049e+06   0.024  0.98082
NameEmpire State Film Production Credit                                                        1.145e+07  9.967e+05  11.485  < 2e-16
NameEmpire State Musical and Theatrical Production Credit                                     -2.342e+05  1.775e+06  -0.132  0.89507
NameExcelsior Jobs Program Credit                                                              1.035e+05  9.545e+05   0.108  0.91366
NameEZ/QEZE Tax Credits - EZ Investment Tax Credit                                             2.752e+06  8.862e+05   3.105  0.00193
NameEZ/QEZE Tax Credits - EZ Wage Tax Credit                                                   4.845e+05  9.213e+05   0.526  0.59899
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes                                  1.245e+06  9.239e+05   1.348  0.17785
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes For Corporate Partners          -1.025e+05  9.549e+05  -0.107  0.91455
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit                                           -6.145e+04  9.387e+05  -0.065  0.94781
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit For Corporate Partners                     9.119e+04  1.044e+06   0.087  0.93038
NameFarm Workforce Retention Credit                                                           -7.802e+03  1.285e+06  -0.006  0.99516
NameFarmers' School Tax Credit                                                                 1.440e+05  1.021e+06   0.141  0.88786
NameHire a Veteran Credit                                                                     -1.238e+06  1.782e+06  -0.695  0.48721
NameHistoric Properties Rehabilitation Credit                                                  1.352e+06  1.055e+06   1.282  0.20015
NameIndustrial or Manufacturing Business Tax Credit                                            4.997e+05  1.074e+06   0.465  0.64173
NameInvestment Tax Credit                                                                      4.463e+05  8.895e+05   0.502  0.61588
NameInvestment Tax Credit for the Financial Services Industry                                  3.976e+05  1.008e+06   0.395  0.69325
NameLife Sciences Research & Development Tax Credit                                           -8.207e+04  2.099e+06  -0.039  0.96882
NameLong-Term Care Insurance Credit                                                            1.246e+05  9.808e+05   0.127  0.89892
NameLow-Income Housing Credit                                                                 -2.764e+04  1.113e+06  -0.025  0.98020
NameMinimum Wage Reimbursement Credit                                                         -2.931e+05  1.006e+06  -0.291  0.77075
NameMortgage Servicing Tax Credit                                                             -4.540e+05  1.085e+06  -0.418  0.67565
NameNew York Youth Jobs Program Tax Credit                                                    -2.587e+05  9.381e+05  -0.276  0.78279
NameQETC Capital Tax Credit                                                                    2.616e+05  1.386e+06   0.189  0.85032
NameQETC Employment Credit                                                                     1.335e+05  1.026e+06   0.130  0.89641
NameQETC Facilities, Operations, and Training Credit                                           5.153e+05  1.918e+06   0.269  0.78820
NameReal Property Tax Relief Credit for Manufacturing                                         -2.635e+05  9.654e+05  -0.273  0.78490
NameSpecial Additional Mortgage Recording Tax Credit                                           3.678e+04  9.244e+05   0.040  0.96827
NameSTART-UP NY Tax Elimination Credit                                                         4.061e+03  1.130e+06   0.004  0.99713
Group1,000,000 - 24,999,999                                                                    2.170e+05  3.501e+05   0.620  0.53548
Group100,000 - 499,999                                                                         1.352e+05  3.579e+05   0.378  0.70572
Group100,000,000 - 499,999,999                                                                 9.644e+05  3.937e+05   2.449  0.01441
Group25,000,000 - 49,999,999                                                                   4.519e+05  4.223e+05   1.070  0.28474
Group50,000,000 - 99,999,999                                                                   4.021e+05  4.235e+05   0.950  0.34247
Group500,000 - 999,999                                                                         2.195e+05  3.880e+05   0.566  0.57170
Group500,000,000 - and over                                                                    3.073e+06  3.846e+05   7.991 2.33e-15
GroupZero or Net Loss                                                                          9.536e+05  3.339e+05   2.856  0.00433
Num                                                                                           -4.520e+02  8.569e+02  -0.527  0.59791
                                                                                                 
(Intercept)                                                                                   *  
Year                                                                                          *  
NameAlternative Fuels and Electric Vehicle Recharging Property Credit                            
NameAlternative Minimum Tax Credit                                                               
NameBeer Production Credit                                                                       
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 6/23/08 but before 7/1/15    
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 7/1/15                    ** 
NameBrownfield Tax Credits - Redevelopment Tax Credit - Prior to 6/23/08                         
NameBrownfield Tax Credits - Remediation Real Property Tax Credit                                
NameClean Heating Fuel Credit                                                                    
NameConservation Easement Tax Credit                                                             
NameCredit for Employment of Persons with Disabilities                                           
NameCredit for Purchase of an Automated External Defibrillator                                   
NameCredit for Taxicabs & Livery Service Vehicles Accessible to Persons with Disabilities        
NameEmpire State Apprentice Tax Credit                                                           
NameEmpire State Commercial Production Credit                                                    
NameEmpire State Film Post Production Credit                                                     
NameEmpire State Film Production Credit                                                       ***
NameEmpire State Musical and Theatrical Production Credit                                        
NameExcelsior Jobs Program Credit                                                                
NameEZ/QEZE Tax Credits - EZ Investment Tax Credit                                            ** 
NameEZ/QEZE Tax Credits - EZ Wage Tax Credit                                                     
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes                                    
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes For Corporate Partners             
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit                                              
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit For Corporate Partners                       
NameFarm Workforce Retention Credit                                                              
NameFarmers' School Tax Credit                                                                   
NameHire a Veteran Credit                                                                        
NameHistoric Properties Rehabilitation Credit                                                    
NameIndustrial or Manufacturing Business Tax Credit                                              
NameInvestment Tax Credit                                                                        
NameInvestment Tax Credit for the Financial Services Industry                                    
NameLife Sciences Research & Development Tax Credit                                              
NameLong-Term Care Insurance Credit                                                              
NameLow-Income Housing Credit                                                                    
NameMinimum Wage Reimbursement Credit                                                            
NameMortgage Servicing Tax Credit                                                                
NameNew York Youth Jobs Program Tax Credit                                                       
NameQETC Capital Tax Credit                                                                      
NameQETC Employment Credit                                                                       
NameQETC Facilities, Operations, and Training Credit                                             
NameReal Property Tax Relief Credit for Manufacturing                                            
NameSpecial Additional Mortgage Recording Tax Credit                                             
NameSTART-UP NY Tax Elimination Credit                                                           
Group1,000,000 - 24,999,999                                                                      
Group100,000 - 499,999                                                                           
Group100,000,000 - 499,999,999                                                                *  
Group25,000,000 - 49,999,999                                                                     
Group50,000,000 - 99,999,999                                                                     
Group500,000 - 999,999                                                                           
Group500,000,000 - and over                                                                   ***
GroupZero or Net Loss                                                                         ** 
Num                                                                                              
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3868000 on 1867 degrees of freedom
Multiple R-squared:  0.2361,    Adjusted R-squared:  0.2144 
F-statistic: 10.88 on 53 and 1867 DF,  p-value: < 2.2e-16

          GVIF Df GVIF^(1/(2*Df))
Year  2.125869  1        1.458036
Name  3.521453 43        1.014746
Group 1.510763  8        1.026124
Num   1.645484  1        1.282764

income.model <- lm(sat.formula, data = income_cleaned)

sat.model.summary(industry_cleaned, sat.field, sat.formula)

    Shapiro-Wilk normality test

data:  df[[field]]
W = 0.22287, p-value < 2.2e-16

[1] "kurtosis"
[1] 135.5482

Call:
lm(formula = sat.formula, data = df)

Residuals:
      Min        1Q    Median        3Q       Max 
-11581741   -371031    -23164    154182  28917959 

Coefficients:
                                                                                                Estimate Std. Error t value Pr(>|t|)
(Intercept)                                                                                   -3.926e+07  2.051e+07  -1.914 0.055677
Year                                                                                           1.936e+04  1.016e+04   1.905 0.056959
NameAlternative Fuels and Electric Vehicle Recharging Property Credit                          5.584e+04  5.062e+05   0.110 0.912180
NameAlternative Minimum Tax Credit                                                             3.523e+05  4.208e+05   0.837 0.402556
NameBeer Production Credit                                                                     8.799e+04  6.261e+05   0.141 0.888249
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 6/23/08 but before 7/1/15  1.919e+06  4.473e+05   4.290 1.86e-05
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 7/1/15                     4.064e+06  7.278e+05   5.584 2.62e-08
NameBrownfield Tax Credits - Redevelopment Tax Credit - Prior to 6/23/08                       1.054e+06  4.779e+05   2.206 0.027462
NameBrownfield Tax Credits - Remediation Real Property Tax Credit                              1.327e+05  4.760e+05   0.279 0.780429
NameClean Heating Fuel Credit                                                                  2.785e+05  4.595e+05   0.606 0.544549
NameConservation Easement Tax Credit                                                           2.743e+04  4.700e+05   0.058 0.953457
NameCredit for Employment of Persons with Disabilities                                         1.574e+05  5.069e+05   0.311 0.756142
NameCredit for Purchase of an Automated External Defibrillator                                 1.082e+05  4.465e+05   0.242 0.808639
NameCredit for Taxicabs & Livery Service Vehicles Accessible to Persons with Disabilities      2.090e+05  8.286e+05   0.252 0.800866
NameEmpire State Apprentice Tax Credit                                                        -3.324e+05  1.012e+06  -0.329 0.742537
NameEmpire State Commercial Production Credit                                                  3.524e+05  6.172e+05   0.571 0.568123
NameEmpire State Film Post Production Credit                                                   5.332e+05  5.224e+05   1.021 0.307585
NameEmpire State Film Production Credit                                                        1.170e+07  4.785e+05  24.458  < 2e-16
NameEmpire State Musical and Theatrical Production Credit                                      7.676e+04  9.010e+05   0.085 0.932112
NameExcelsior Jobs Program Credit                                                              7.086e+05  4.393e+05   1.613 0.106849
NameEZ/QEZE Tax Credits - EZ Investment Tax Credit                                             1.381e+06  4.318e+05   3.199 0.001399
NameEZ/QEZE Tax Credits - EZ Wage Tax Credit                                                   3.715e+05  4.213e+05   0.882 0.377942
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes                                  1.160e+06  4.192e+05   2.767 0.005700
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes For Corporate Partners           3.634e+05  4.311e+05   0.843 0.399359
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit                                            2.567e+05  4.265e+05   0.602 0.547350
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit For Corporate Partners                     7.379e+04  5.041e+05   0.146 0.883634
NameFarm Workforce Retention Credit                                                            2.727e+04  5.352e+05   0.051 0.959361
NameFarmers' School Tax Credit                                                                 1.287e+05  5.133e+05   0.251 0.802102
NameHire a Veteran Credit                                                                      1.459e+05  8.253e+05   0.177 0.859709
NameHistoric Properties Rehabilitation Credit                                                  1.875e+06  4.841e+05   3.874 0.000110
NameInvestment Tax Credit                                                                      7.182e+05  4.129e+05   1.739 0.082075
NameInvestment Tax Credit for the Financial Services Industry                                  6.339e+05  5.757e+05   1.101 0.270913
NameLife Sciences Research & Development Tax Credit                                           -2.243e+03  9.007e+05  -0.002 0.998014
NameLong-Term Care Insurance Credit                                                            1.385e+05  4.200e+05   0.330 0.741537
NameLow-Income Housing Credit                                                                  1.642e+06  5.494e+05   2.988 0.002833
NameMinimum Wage Reimbursement Credit                                                          9.624e+04  4.381e+05   0.220 0.826159
NameMortgage Servicing Tax Credit                                                              2.077e+05  6.462e+05   0.321 0.747934
NameNew York Youth Jobs Program Tax Credit                                                     1.953e+05  4.273e+05   0.457 0.647604
NameQETC Capital Tax Credit                                                                    2.986e+05  5.868e+05   0.509 0.610823
NameQETC Employment Credit                                                                     8.982e+04  4.465e+05   0.201 0.840607
NameQETC Facilities, Operations, and Training Credit                                           3.477e+05  6.711e+05   0.518 0.604441
NameReal Property Tax Relief Credit for Manufacturing                                          1.520e+05  4.423e+05   0.344 0.731171
NameSpecial Additional Mortgage Recording Tax Credit                                           2.609e+05  4.432e+05   0.589 0.556155
NameSTART-UP NY Tax Elimination Credit                                                         1.703e+04  4.750e+05   0.036 0.971411
GroupAdministrative and Support and Waste Management and Remediation Services                 -2.280e+03  2.519e+05  -0.009 0.992777
GroupAdministrative/Support/Waste Management/Remediation Services                             -3.173e+03  2.798e+05  -0.011 0.990952
GroupAgriculture, Forestry, Fishing and Hunting                                                7.269e+04  2.330e+05   0.312 0.755097
GroupArts, Entertainment, and Recreation                                                       5.866e+05  2.317e+05   2.532 0.011408
GroupConstruction                                                                             -1.699e+04  2.171e+05  -0.078 0.937621
GroupEducational Services                                                                      5.569e+04  2.948e+05   0.189 0.850176
GroupFinance and Insurance                                                                     2.139e+05  2.034e+05   1.051 0.293237
GroupHealth Care and Social Assistance                                                         1.300e+04  2.290e+05   0.057 0.954731
GroupInformation                                                                              -2.433e+05  2.178e+05  -1.117 0.263917
GroupManagement of Companies and Enterprises                                                   3.355e+05  1.949e+05   1.721 0.085332
GroupManufacturing                                                                             6.786e+05  2.028e+05   3.346 0.000831
GroupMining                                                                                   -1.561e+04  3.593e+05  -0.043 0.965352
GroupMining, Quarrying, and Oil and Gas Extraction                                             1.084e+05  3.011e+05   0.360 0.718901
GroupOther Services (except Public Administration)                                            -6.462e+04  2.217e+05  -0.291 0.770697
GroupProfessional, Scientific, and Technical Services                                          3.736e+05  2.085e+05   1.792 0.073214
GroupReal Estate and Rental and Leasing                                                        9.506e+04  2.044e+05   0.465 0.641882
GroupRetail Trade                                                                              4.746e+04  2.036e+05   0.233 0.815756
GroupTransportation and Warehousing                                                           -1.866e+04  2.300e+05  -0.081 0.935321
GroupUtilities                                                                                 5.308e+05  2.633e+05   2.016 0.043917
GroupWholesale Trade                                                                           6.106e+04  2.081e+05   0.293 0.769261
Num                                                                                           -9.657e+02  4.272e+02  -2.260 0.023889
                                                                                                 
(Intercept)                                                                                   .  
Year                                                                                          .  
NameAlternative Fuels and Electric Vehicle Recharging Property Credit                            
NameAlternative Minimum Tax Credit                                                               
NameBeer Production Credit                                                                       
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 6/23/08 but before 7/1/15 ***
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 7/1/15                    ***
NameBrownfield Tax Credits - Redevelopment Tax Credit - Prior to 6/23/08                      *  
NameBrownfield Tax Credits - Remediation Real Property Tax Credit                                
NameClean Heating Fuel Credit                                                                    
NameConservation Easement Tax Credit                                                             
NameCredit for Employment of Persons with Disabilities                                           
NameCredit for Purchase of an Automated External Defibrillator                                   
NameCredit for Taxicabs & Livery Service Vehicles Accessible to Persons with Disabilities        
NameEmpire State Apprentice Tax Credit                                                           
NameEmpire State Commercial Production Credit                                                    
NameEmpire State Film Post Production Credit                                                     
NameEmpire State Film Production Credit                                                       ***
NameEmpire State Musical and Theatrical Production Credit                                        
NameExcelsior Jobs Program Credit                                                                
NameEZ/QEZE Tax Credits - EZ Investment Tax Credit                                            ** 
NameEZ/QEZE Tax Credits - EZ Wage Tax Credit                                                     
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes                                 ** 
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes For Corporate Partners             
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit                                              
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit For Corporate Partners                       
NameFarm Workforce Retention Credit                                                              
NameFarmers' School Tax Credit                                                                   
NameHire a Veteran Credit                                                                        
NameHistoric Properties Rehabilitation Credit                                                 ***
NameInvestment Tax Credit                                                                     .  
NameInvestment Tax Credit for the Financial Services Industry                                    
NameLife Sciences Research & Development Tax Credit                                              
NameLong-Term Care Insurance Credit                                                              
NameLow-Income Housing Credit                                                                 ** 
NameMinimum Wage Reimbursement Credit                                                            
NameMortgage Servicing Tax Credit                                                                
NameNew York Youth Jobs Program Tax Credit                                                       
NameQETC Capital Tax Credit                                                                      
NameQETC Employment Credit                                                                       
NameQETC Facilities, Operations, and Training Credit                                             
NameReal Property Tax Relief Credit for Manufacturing                                            
NameSpecial Additional Mortgage Recording Tax Credit                                             
NameSTART-UP NY Tax Elimination Credit                                                           
GroupAdministrative and Support and Waste Management and Remediation Services                    
GroupAdministrative/Support/Waste Management/Remediation Services                                
GroupAgriculture, Forestry, Fishing and Hunting                                                  
GroupArts, Entertainment, and Recreation                                                      *  
GroupConstruction                                                                                
GroupEducational Services                                                                        
GroupFinance and Insurance                                                                       
GroupHealth Care and Social Assistance                                                           
GroupInformation                                                                                 
GroupManagement of Companies and Enterprises                                                  .  
GroupManufacturing                                                                            ***
GroupMining                                                                                      
GroupMining, Quarrying, and Oil and Gas Extraction                                               
GroupOther Services (except Public Administration)                                               
GroupProfessional, Scientific, and Technical Services                                         .  
GroupReal Estate and Rental and Leasing                                                          
GroupRetail Trade                                                                                
GroupTransportation and Warehousing                                                              
GroupUtilities                                                                                *  
GroupWholesale Trade                                                                             
Num                                                                                           *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1612000 on 2411 degrees of freedom
Multiple R-squared:  0.4674,    Adjusted R-squared:  0.4533 
F-statistic: 33.06 on 64 and 2411 DF,  p-value: < 2.2e-16

          GVIF Df GVIF^(1/(2*Df))
Year  2.190806  1        1.480137
Name  5.185764 42        1.019787
Group 2.724217 20        1.025371
Num   1.370920  1        1.170863

industry.model <- lm(sat.formula, data = industry_cleaned)

Correcting violation of Normality in previous model with BoxCox transform

bc_func <- function (lm.cleaned, lambda.range){
  bc = boxCox(lm.cleaned, lambda = lambda.range)
  #Extracting the best lambda value.
  return(bc$x[which(bc$y == max(bc$y))])
}
  
#Income Group Dataset
income.lambda.bc = bc_func(income.model, seq(-0.2, 0.2, 1/10))

income.lambda.bc
[1] -0.01414141
#Industry Group Dataset
industry.lambda.bc = bc_func(industry.model, seq(-0.2, 0.2, 1/10))

industry.lambda.bc
[1] -0.03434343
bc_transform <- function(df, lambda.bc){
  return (df %>% 
            mutate(Avg.bc = (Avg^lambda.bc -1)/lambda.bc) %>% 
            select(-c(Avg, Amount)))
}

#Income Group Dataset
income_cleaned_bc <- bc_transform(income_cleaned, income.lambda.bc)
income.model.bc = lm(Avg.bc ~ ., data = income_cleaned_bc)

#Industry Group Dataset
industry_cleaned_bc <- bc_transform(industry_cleaned, industry.lambda.bc)
industry.model.bc = lm(Avg.bc ~ ., data = industry_cleaned_bc)

Checking linear regression assumptions for the transformed data.

sat.formula.bc <- Avg.bc ~ .
sat.field.bc <- 'Avg.bc'

#Income
sat.model.summary(income_cleaned_bc, sat.field.bc, sat.formula.bc)

    Shapiro-Wilk normality test

data:  df[[field]]
W = 0.99696, p-value = 0.000782

[1] "kurtosis"
[1] -0.2553313

Call:
lm(formula = sat.formula, data = df)

Residuals:
    Min      1Q  Median      3Q     Max 
-6.6597 -0.5738 -0.0113  0.5668  4.4826 

Coefficients:
                                                                                                Estimate Std. Error t value Pr(>|t|)
(Intercept)                                                                                   -3.634e+01  1.456e+01  -2.496 0.012643
Year                                                                                           2.288e-02  7.214e-03   3.171 0.001543
NameAlternative Fuels and Electric Vehicle Recharging Property Credit                         -8.643e-01  3.281e-01  -2.634 0.008510
NameAlternative Minimum Tax Credit                                                            -2.052e+00  2.577e-01  -7.962 2.91e-15
NameBeer Production Credit                                                                     5.687e-01  3.407e-01   1.669 0.095234
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 6/23/08 but before 7/1/15  1.715e+00  2.630e-01   6.521 8.99e-11
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 7/1/15                     2.676e+00  3.754e-01   7.130 1.43e-12
NameBrownfield Tax Credits - Redevelopment Tax Credit - Prior to 6/23/08                       1.331e+00  2.622e-01   5.076 4.24e-07
NameBrownfield Tax Credits - Remediation Real Property Tax Credit                              5.458e-02  2.620e-01   0.208 0.834991
NameClean Heating Fuel Credit                                                                 -3.086e+00  2.705e-01 -11.409  < 2e-16
NameConservation Easement Tax Credit                                                          -2.137e+00  2.810e-01  -7.606 4.45e-14
NameCredit for Employment of Persons with Disabilities                                        -3.118e+00  2.956e-01 -10.547  < 2e-16
NameCredit for Purchase of an Automated External Defibrillator                                -2.938e+00  2.560e-01 -11.473  < 2e-16
NameCredit for Taxicabs & Livery Service Vehicles Accessible to Persons with Disabilities     -5.673e-01  4.698e-01  -1.207 0.227430
NameEmpire State Apprentice Tax Credit                                                        -2.207e+00  4.024e-01  -5.485 4.71e-08
NameEmpire State Commercial Production Credit                                                  6.075e-02  3.410e-01   0.178 0.858634
NameEmpire State Film Post Production Credit                                                   1.101e+00  2.769e-01   3.977 7.25e-05
NameEmpire State Film Production Credit                                                        2.853e+00  2.632e-01  10.838  < 2e-16
NameEmpire State Musical and Theatrical Production Credit                                      2.508e-01  4.688e-01   0.535 0.592803
NameExcelsior Jobs Program Credit                                                              4.651e-01  2.521e-01   1.845 0.065178
NameEZ/QEZE Tax Credits - EZ Investment Tax Credit                                             8.876e-01  2.341e-01   3.792 0.000154
NameEZ/QEZE Tax Credits - EZ Wage Tax Credit                                                   1.775e-01  2.433e-01   0.730 0.465701
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes                                  1.220e+00  2.440e-01   5.000 6.26e-07
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes For Corporate Partners           1.182e-01  2.522e-01   0.469 0.639260
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit                                           -8.497e-01  2.479e-01  -3.427 0.000623
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit For Corporate Partners                    -1.358e+00  2.756e-01  -4.928 9.02e-07
NameFarm Workforce Retention Credit                                                           -1.612e+00  3.394e-01  -4.749 2.20e-06
NameFarmers' School Tax Credit                                                                -1.311e+00  2.696e-01  -4.863 1.26e-06
NameHire a Veteran Credit                                                                     -2.915e+00  4.706e-01  -6.195 7.15e-10
NameHistoric Properties Rehabilitation Credit                                                  1.918e+00  2.786e-01   6.886 7.81e-12
NameIndustrial or Manufacturing Business Tax Credit                                           -1.718e+00  2.836e-01  -6.059 1.66e-09
NameInvestment Tax Credit                                                                      7.147e-02  2.349e-01   0.304 0.760985
NameInvestment Tax Credit for the Financial Services Industry                                  3.176e-01  2.662e-01   1.193 0.232870
NameLife Sciences Research & Development Tax Credit                                            7.033e-01  5.543e-01   1.269 0.204728
NameLong-Term Care Insurance Credit                                                           -2.863e+00  2.590e-01 -11.051  < 2e-16
NameLow-Income Housing Credit                                                                 -9.063e-01  2.940e-01  -3.083 0.002080
NameMinimum Wage Reimbursement Credit                                                         -1.241e+00  2.656e-01  -4.674 3.17e-06
NameMortgage Servicing Tax Credit                                                             -9.378e-01  2.865e-01  -3.273 0.001084
NameNew York Youth Jobs Program Tax Credit                                                    -1.330e+00  2.478e-01  -5.367 9.01e-08
NameQETC Capital Tax Credit                                                                    4.561e-01  3.661e-01   1.246 0.212956
NameQETC Employment Credit                                                                    -5.888e-01  2.709e-01  -2.174 0.029855
NameQETC Facilities, Operations, and Training Credit                                           5.799e-01  5.065e-01   1.145 0.252462
NameReal Property Tax Relief Credit for Manufacturing                                         -1.518e+00  2.550e-01  -5.956 3.09e-09
NameSpecial Additional Mortgage Recording Tax Credit                                          -2.309e-01  2.441e-01  -0.946 0.344374
NameSTART-UP NY Tax Elimination Credit                                                        -2.193e+00  2.985e-01  -7.345 3.05e-13
Group1,000,000 - 24,999,999                                                                    1.090e+00  9.246e-02  11.785  < 2e-16
Group100,000 - 499,999                                                                         3.590e-01  9.451e-02   3.798 0.000150
Group100,000,000 - 499,999,999                                                                 1.685e+00  1.040e-01  16.202  < 2e-16
Group25,000,000 - 49,999,999                                                                   1.325e+00  1.115e-01  11.883  < 2e-16
Group50,000,000 - 99,999,999                                                                   1.473e+00  1.118e-01  13.172  < 2e-16
Group500,000 - 999,999                                                                         6.032e-01  1.025e-01   5.886 4.67e-09
Group500,000,000 - and over                                                                    2.332e+00  1.016e-01  22.953  < 2e-16
GroupZero or Net Loss                                                                          9.934e-01  8.817e-02  11.267  < 2e-16
Num                                                                                           -1.533e-03  2.263e-04  -6.775 1.66e-11
                                                                                                 
(Intercept)                                                                                   *  
Year                                                                                          ** 
NameAlternative Fuels and Electric Vehicle Recharging Property Credit                         ** 
NameAlternative Minimum Tax Credit                                                            ***
NameBeer Production Credit                                                                    .  
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 6/23/08 but before 7/1/15 ***
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 7/1/15                    ***
NameBrownfield Tax Credits - Redevelopment Tax Credit - Prior to 6/23/08                      ***
NameBrownfield Tax Credits - Remediation Real Property Tax Credit                                
NameClean Heating Fuel Credit                                                                 ***
NameConservation Easement Tax Credit                                                          ***
NameCredit for Employment of Persons with Disabilities                                        ***
NameCredit for Purchase of an Automated External Defibrillator                                ***
NameCredit for Taxicabs & Livery Service Vehicles Accessible to Persons with Disabilities        
NameEmpire State Apprentice Tax Credit                                                        ***
NameEmpire State Commercial Production Credit                                                    
NameEmpire State Film Post Production Credit                                                  ***
NameEmpire State Film Production Credit                                                       ***
NameEmpire State Musical and Theatrical Production Credit                                        
NameExcelsior Jobs Program Credit                                                             .  
NameEZ/QEZE Tax Credits - EZ Investment Tax Credit                                            ***
NameEZ/QEZE Tax Credits - EZ Wage Tax Credit                                                     
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes                                 ***
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes For Corporate Partners             
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit                                           ***
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit For Corporate Partners                    ***
NameFarm Workforce Retention Credit                                                           ***
NameFarmers' School Tax Credit                                                                ***
NameHire a Veteran Credit                                                                     ***
NameHistoric Properties Rehabilitation Credit                                                 ***
NameIndustrial or Manufacturing Business Tax Credit                                           ***
NameInvestment Tax Credit                                                                        
NameInvestment Tax Credit for the Financial Services Industry                                    
NameLife Sciences Research & Development Tax Credit                                              
NameLong-Term Care Insurance Credit                                                           ***
NameLow-Income Housing Credit                                                                 ** 
NameMinimum Wage Reimbursement Credit                                                         ***
NameMortgage Servicing Tax Credit                                                             ** 
NameNew York Youth Jobs Program Tax Credit                                                    ***
NameQETC Capital Tax Credit                                                                      
NameQETC Employment Credit                                                                    *  
NameQETC Facilities, Operations, and Training Credit                                             
NameReal Property Tax Relief Credit for Manufacturing                                         ***
NameSpecial Additional Mortgage Recording Tax Credit                                             
NameSTART-UP NY Tax Elimination Credit                                                        ***
Group1,000,000 - 24,999,999                                                                   ***
Group100,000 - 499,999                                                                        ***
Group100,000,000 - 499,999,999                                                                ***
Group25,000,000 - 49,999,999                                                                  ***
Group50,000,000 - 99,999,999                                                                  ***
Group500,000 - 999,999                                                                        ***
Group500,000,000 - and over                                                                   ***
GroupZero or Net Loss                                                                         ***
Num                                                                                           ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.022 on 1867 degrees of freedom
Multiple R-squared:  0.7368,    Adjusted R-squared:  0.7293 
F-statistic: 98.61 on 53 and 1867 DF,  p-value: < 2.2e-16

          GVIF Df GVIF^(1/(2*Df))
Year  2.125869  1        1.458036
Name  3.521453 43        1.014746
Group 1.510763  8        1.026124
Num   1.645484  1        1.282764

#Industry
sat.model.summary(industry_cleaned_bc, sat.field.bc, sat.formula.bc)

    Shapiro-Wilk normality test

data:  df[[field]]
W = 0.9902, p-value = 5.826e-12

[1] "kurtosis"
[1] -0.4869026

Call:
lm(formula = sat.formula, data = df)

Residuals:
    Min      1Q  Median      3Q     Max 
-6.2888 -0.4697  0.0183  0.4928  3.9068 

Coefficients:
                                                                                                Estimate Std. Error t value Pr(>|t|)
(Intercept)                                                                                   -6.095e+01  1.107e+01  -5.505 4.09e-08
Year                                                                                           3.440e-02  5.488e-03   6.269 4.30e-10
NameAlternative Fuels and Electric Vehicle Recharging Property Credit                          2.665e-01  2.733e-01   0.975 0.329737
NameAlternative Minimum Tax Credit                                                            -2.463e+00  2.272e-01 -10.839  < 2e-16
NameBeer Production Credit                                                                     6.334e-01  3.381e-01   1.873 0.061126
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 6/23/08 but before 7/1/15  2.198e+00  2.415e-01   9.100  < 2e-16
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 7/1/15                     2.727e+00  3.930e-01   6.939 5.06e-12
NameBrownfield Tax Credits - Redevelopment Tax Credit - Prior to 6/23/08                       1.586e+00  2.581e-01   6.148 9.17e-10
NameBrownfield Tax Credits - Remediation Real Property Tax Credit                              9.695e-01  2.570e-01   3.772 0.000166
NameClean Heating Fuel Credit                                                                 -2.544e+00  2.481e-01 -10.252  < 2e-16
NameConservation Easement Tax Credit                                                          -1.123e+00  2.538e-01  -4.423 1.02e-05
NameCredit for Employment of Persons with Disabilities                                        -1.245e+00  2.737e-01  -4.549 5.67e-06
NameCredit for Purchase of an Automated External Defibrillator                                -1.535e+00  2.411e-01  -6.368 2.29e-10
NameCredit for Taxicabs & Livery Service Vehicles Accessible to Persons with Disabilities     -8.171e-02  4.474e-01  -0.183 0.855119
NameEmpire State Apprentice Tax Credit                                                        -8.683e-01  5.464e-01  -1.589 0.112125
NameEmpire State Commercial Production Credit                                                  6.235e-01  3.333e-01   1.871 0.061481
NameEmpire State Film Post Production Credit                                                   1.439e+00  2.821e-01   5.100 3.66e-07
NameEmpire State Film Production Credit                                                        3.232e+00  2.584e-01  12.509  < 2e-16
NameEmpire State Musical and Theatrical Production Credit                                      1.012e+00  4.865e-01   2.080 0.037608
NameExcelsior Jobs Program Credit                                                              1.643e+00  2.372e-01   6.929 5.42e-12
NameEZ/QEZE Tax Credits - EZ Investment Tax Credit                                             1.310e+00  2.332e-01   5.617 2.17e-08
NameEZ/QEZE Tax Credits - EZ Wage Tax Credit                                                   7.127e-01  2.275e-01   3.133 0.001750
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes                                  1.707e+00  2.264e-01   7.540 6.61e-14
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes For Corporate Partners           9.777e-01  2.328e-01   4.200 2.77e-05
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit                                            1.609e-01  2.303e-01   0.699 0.484921
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit For Corporate Partners                    -5.241e-01  2.722e-01  -1.925 0.054320
NameFarm Workforce Retention Credit                                                           -8.623e-01  2.890e-01  -2.984 0.002876
NameFarmers' School Tax Credit                                                                -1.158e+00  2.771e-01  -4.179 3.03e-05
NameHire a Veteran Credit                                                                     -1.040e+00  4.456e-01  -2.335 0.019638
NameHistoric Properties Rehabilitation Credit                                                  2.397e+00  2.614e-01   9.172  < 2e-16
NameInvestment Tax Credit                                                                      6.981e-01  2.230e-01   3.131 0.001763
NameInvestment Tax Credit for the Financial Services Industry                                  1.560e+00  3.108e-01   5.019 5.59e-07
NameLife Sciences Research & Development Tax Credit                                            9.057e-01  4.864e-01   1.862 0.062697
NameLong-Term Care Insurance Credit                                                           -1.867e+00  2.268e-01  -8.231 3.01e-16
NameLow-Income Housing Credit                                                                  1.331e+00  2.967e-01   4.487 7.57e-06
NameMinimum Wage Reimbursement Credit                                                         -9.161e-01  2.366e-01  -3.872 0.000111
NameMortgage Servicing Tax Credit                                                              8.932e-01  3.489e-01   2.560 0.010534
NameNew York Youth Jobs Program Tax Credit                                                     1.263e-01  2.307e-01   0.548 0.584069
NameQETC Capital Tax Credit                                                                    1.162e+00  3.168e-01   3.667 0.000251
NameQETC Employment Credit                                                                    -3.048e-01  2.411e-01  -1.264 0.206249
NameQETC Facilities, Operations, and Training Credit                                           1.147e+00  3.624e-01   3.165 0.001571
NameReal Property Tax Relief Credit for Manufacturing                                         -6.559e-01  2.388e-01  -2.746 0.006077
NameSpecial Additional Mortgage Recording Tax Credit                                           7.505e-01  2.393e-01   3.136 0.001736
NameSTART-UP NY Tax Elimination Credit                                                        -1.834e+00  2.565e-01  -7.151 1.14e-12
GroupAdministrative and Support and Waste Management and Remediation Services                  2.878e-01  1.360e-01   2.116 0.034417
GroupAdministrative/Support/Waste Management/Remediation Services                              1.675e-01  1.511e-01   1.109 0.267612
GroupAgriculture, Forestry, Fishing and Hunting                                               -1.132e-01  1.258e-01  -0.899 0.368486
GroupArts, Entertainment, and Recreation                                                       5.595e-01  1.251e-01   4.473 8.09e-06
GroupConstruction                                                                             -4.299e-02  1.172e-01  -0.367 0.713860
GroupEducational Services                                                                      2.253e-01  1.592e-01   1.415 0.157160
GroupFinance and Insurance                                                                     5.350e-01  1.099e-01   4.870 1.19e-06
GroupHealth Care and Social Assistance                                                        -6.777e-02  1.237e-01  -0.548 0.583720
GroupInformation                                                                               7.098e-01  1.176e-01   6.037 1.81e-09
GroupManagement of Companies and Enterprises                                                   6.672e-01  1.052e-01   6.340 2.73e-10
GroupManufacturing                                                                             4.608e-01  1.095e-01   4.208 2.67e-05
GroupMining                                                                                    2.515e-01  1.940e-01   1.296 0.194977
GroupMining, Quarrying, and Oil and Gas Extraction                                             3.869e-01  1.626e-01   2.379 0.017421
GroupOther Services (except Public Administration)                                            -1.550e-01  1.197e-01  -1.295 0.195482
GroupProfessional, Scientific, and Technical Services                                          4.875e-01  1.126e-01   4.331 1.55e-05
GroupReal Estate and Rental and Leasing                                                        1.461e-01  1.104e-01   1.324 0.185596
GroupRetail Trade                                                                              3.754e-01  1.100e-01   3.414 0.000650
GroupTransportation and Warehousing                                                            2.125e-01  1.242e-01   1.711 0.087179
GroupUtilities                                                                                 6.972e-01  1.422e-01   4.904 1.00e-06
GroupWholesale Trade                                                                           4.367e-01  1.124e-01   3.886 0.000105
Num                                                                                            4.542e-04  2.307e-04   1.969 0.049082
                                                                                                 
(Intercept)                                                                                   ***
Year                                                                                          ***
NameAlternative Fuels and Electric Vehicle Recharging Property Credit                            
NameAlternative Minimum Tax Credit                                                            ***
NameBeer Production Credit                                                                    .  
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 6/23/08 but before 7/1/15 ***
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 7/1/15                    ***
NameBrownfield Tax Credits - Redevelopment Tax Credit - Prior to 6/23/08                      ***
NameBrownfield Tax Credits - Remediation Real Property Tax Credit                             ***
NameClean Heating Fuel Credit                                                                 ***
NameConservation Easement Tax Credit                                                          ***
NameCredit for Employment of Persons with Disabilities                                        ***
NameCredit for Purchase of an Automated External Defibrillator                                ***
NameCredit for Taxicabs & Livery Service Vehicles Accessible to Persons with Disabilities        
NameEmpire State Apprentice Tax Credit                                                           
NameEmpire State Commercial Production Credit                                                 .  
NameEmpire State Film Post Production Credit                                                  ***
NameEmpire State Film Production Credit                                                       ***
NameEmpire State Musical and Theatrical Production Credit                                     *  
NameExcelsior Jobs Program Credit                                                             ***
NameEZ/QEZE Tax Credits - EZ Investment Tax Credit                                            ***
NameEZ/QEZE Tax Credits - EZ Wage Tax Credit                                                  ** 
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes                                 ***
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes For Corporate Partners          ***
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit                                              
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit For Corporate Partners                    .  
NameFarm Workforce Retention Credit                                                           ** 
NameFarmers' School Tax Credit                                                                ***
NameHire a Veteran Credit                                                                     *  
NameHistoric Properties Rehabilitation Credit                                                 ***
NameInvestment Tax Credit                                                                     ** 
NameInvestment Tax Credit for the Financial Services Industry                                 ***
NameLife Sciences Research & Development Tax Credit                                           .  
NameLong-Term Care Insurance Credit                                                           ***
NameLow-Income Housing Credit                                                                 ***
NameMinimum Wage Reimbursement Credit                                                         ***
NameMortgage Servicing Tax Credit                                                             *  
NameNew York Youth Jobs Program Tax Credit                                                       
NameQETC Capital Tax Credit                                                                   ***
NameQETC Employment Credit                                                                       
NameQETC Facilities, Operations, and Training Credit                                          ** 
NameReal Property Tax Relief Credit for Manufacturing                                         ** 
NameSpecial Additional Mortgage Recording Tax Credit                                          ** 
NameSTART-UP NY Tax Elimination Credit                                                        ***
GroupAdministrative and Support and Waste Management and Remediation Services                 *  
GroupAdministrative/Support/Waste Management/Remediation Services                                
GroupAgriculture, Forestry, Fishing and Hunting                                                  
GroupArts, Entertainment, and Recreation                                                      ***
GroupConstruction                                                                                
GroupEducational Services                                                                        
GroupFinance and Insurance                                                                    ***
GroupHealth Care and Social Assistance                                                           
GroupInformation                                                                              ***
GroupManagement of Companies and Enterprises                                                  ***
GroupManufacturing                                                                            ***
GroupMining                                                                                      
GroupMining, Quarrying, and Oil and Gas Extraction                                            *  
GroupOther Services (except Public Administration)                                               
GroupProfessional, Scientific, and Technical Services                                         ***
GroupReal Estate and Rental and Leasing                                                          
GroupRetail Trade                                                                             ***
GroupTransportation and Warehousing                                                           .  
GroupUtilities                                                                                ***
GroupWholesale Trade                                                                          ***
Num                                                                                           *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.8703 on 2411 degrees of freedom
Multiple R-squared:  0.7631,    Adjusted R-squared:  0.7569 
F-statistic: 121.4 on 64 and 2411 DF,  p-value: < 2.2e-16

          GVIF Df GVIF^(1/(2*Df))
Year  2.190806  1        1.480137
Name  5.185764 42        1.019787
Group 2.724217 20        1.025371
Num   1.370920  1        1.170863

BIC comparison before and after BoxCox transform

BIC(income.model.bc, income.model)
BIC(industry.model.bc, industry.model)

Stepwise Regression on Income_cat_bc (boxcox transformed dataset)

#creating dummy variable columns for stepwise
dummy_func <- function (df){
  x = model.matrix(Avg.bc ~., df)[, -1]
  dummy_bc = as.data.frame(x) %>% mutate(Avg.bc = df$Avg.bc)
  colnames(dummy_bc) <- str_replace_all(colnames(dummy_bc), "-|'|/| |,|�|&" , '_')
  return(dummy_bc)
}

Cleaning column names further so stepwise regression doesn’t present any errors

#Income Group Dataset
income.dummy.bc <- dummy_func(income_cleaned_bc)
#colnames(income.dummy.bc)[37] <- 'NameManufactureru0092s_Real_Property_Tax_Credit'
colnames(income.dummy.bc)

#Industry Group Dataset
industry.dummy.bc <- dummy_func(industry_cleaned_bc)
#colnames(industry.dummy.bc)[35] <- 'NameManufactureru0092s_Real_Property_Tax_Credit'
colnames(industry.dummy.bc)

Stepwise regression using BIC as the criteria (the penalty k = log(n)).

#Creating Stepwise Models
bcs = list(income = income.dummy.bc, industry = industry.dummy.bc)
model.fulls = list(income = lm(Avg.bc ~ ., data = income.dummy.bc), industry = lm(Avg.bc ~ ., data = industry.dummy.bc)) #All variables
model.emptys = list(income = lm(Avg.bc ~ 1, data = income.dummy.bc), industry = lm(Avg.bc ~ 1, data = industry.dummy.bc)) #intercept only
k = c('income', 'industry')
forwardBIC = list(income = NULL, industry = NULL)
backwardBIC = list(income = NULL, industry = NULL)

for (i in k){
  bc = bcs[[i]]
  scope = list(lower = formula(model.emptys[[i]]), upper = formula(model.fulls[[i]]))
  n_obs = bc %>% count() %>% dplyr::first()
  forwardBIC[[i]] = step(model.emptys[[i]], scope, direction = "forward", k = log(n_obs))
  backwardBIC[[i]] = step(model.fulls[[i]], scope, direction = "backward", k = log(n_obs))
}

Selecting Best Formula per Dataset from Stepwise Regressions

#anova(model2, model.saturated)

#Income Group Dataset
income.best.formula <- backwardBIC[['income']]$call[[2]]
income.best.formula

#Industry Group Dataset
industry.best.formula <- forwardBIC[['industry']]$call[[2]]
industry.best.formula

Stepwise regression using BIC as the criteria (the penalty k = log(n)).

#checking our selected model's predictor variable's VIFs
vif(backwardBIC)
                                                                                         Year 
                                                                                     1.661856 
                        NameAlternative_Fuels_and_Electric_Vehicle_Recharging_Property_Credit 
                                                                                     1.040066 
                                                           NameAlternative_Minimum_Tax_Credit 
                                                                                     1.355727 
NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___On_or_after_6_23_08_but_before_7_1_15 
                                                                                     1.077139 
                   NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___On_or_after_7_1_15 
                                                                                     1.032409 
                     NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___Prior_to_6_23_08 
                                                                                     1.076724 
                                                                NameClean_Heating_Fuel_Credit 
                                                                                     1.086361 
                                                         NameConservation_Easement_Tax_Credit 
                                                                                     1.071241 
                                       NameCredit_for_Employment_of_Persons_with_Disabilities 
                                                                                     1.050364 
                               NameCredit_for_Purchase_of_an_Automated_External_Defibrillator 
                                                                                     1.084252 
                                                       NameEmpire_State_Apprentice_Tax_Credit 
                                                                                     1.028286 
                                                 NameEmpire_State_Film_Post_Production_Credit 
                                                                                     1.067360 
                                                      NameEmpire_State_Film_Production_Credit 
                                                                                     1.079378 
                                           NameEZ_QEZE_Tax_Credits___EZ_Investment_Tax_Credit 
                                                                                     1.203345 
                                NameEZ_QEZE_Tax_Credits___QEZE_Credit_for_Real_Property_Taxes 
                                                                                     1.110401 
                                          NameEZ_QEZE_Tax_Credits___QEZE_Tax_Reduction_Credit 
                                                                                     1.094191 
                   NameEZ_QEZE_Tax_Credits___QEZE_Tax_Reduction_Credit_For_Corporate_Partners 
                                                                                     1.059267 
                                                          NameFarm_Workforce_Retention_Credit 
                                                                                     1.043336 
                                                               NameFarmers__School_Tax_Credit 
                                                                                     1.075009 
                                                                    NameHire_a_Veteran_Credit 
                                                                                     1.016637 
                                                NameHistoric_Properties_Rehabilitation_Credit 
                                                                                     1.066991 
                                          NameIndustrial_or_Manufacturing_Business_Tax_Credit 
                                                                                     1.180919 
                                                          NameLong_Term_Care_Insurance_Credit 
                                                                                     1.085593 
                                                                NameLow_Income_Housing_Credit 
                                                                                     1.059690 
                                              NameManufactureru0092s_Real_Property_Tax_Credit 
                                                                                     1.059324 
                                                  NameManufacturer_s_Real_Property_Tax_Credit 
                                                                                     1.051337 
                                                        NameMinimum_Wage_Reimbursement_Credit 
                                                                                     1.074669 
                                                            NameMortgage_Servicing_Tax_Credit 
                                                                                     1.068997 
                                                   NameNew_York_Youth_Jobs_Program_Tax_Credit 
                                                                                     1.109900 
                                                                   NameQETC_Employment_Credit 
                                                                                     1.072612 
                                         NameSpecial_Additional_Mortgage_Recording_Tax_Credit 
                                                                                     1.114775 
                                                       NameSTART_UP_NY_Tax_Elimination_Credit 
                                                                                     1.055977 
                                                                    ENI1_000_000___24_999_999 
                                                                                     1.850053 
                                                                         ENI100_000___499_999 
                                                                                     1.795816 
                                                                 ENI100_000_000___499_999_999 
                                                                                     1.691776 
                                                                   ENI25_000_000___49_999_999 
                                                                                     1.578815 
                                                                   ENI50_000_000___99_999_999 
                                                                                     1.576866 
                                                                         ENI500_000___999_999 
                                                                                     1.708105 
                                                                    ENI500_000_000___and_over 
                                                                                     1.744570 
                                                                          ENIZero_or_Net_Loss 
                                                                                     1.867768 
                                                                                          Num 
                                                                                     1.533625 

Splitting data up into test data and training data (test data is for year 2019, training is the rest)

dim(income.data.split)
NULL

Lasso regression for comparison to backward stepwise

for (i in k){
  X.train <- xy.splits[[i]][['X.train']]
  y.train <- xy.splits[[i]][['y.train']]
  X.test <- xy.splits[[i]][['X.test']]
  y.test <- xy.splits[[i]][['y.test']]
  
  #create lambda grid
  lambda.grid = 10^seq(2, -5, length = 100)
  
  #create lasso models with lambda.grid
  lasso.models = glmnet(X.train, y.train, alpha = 1, lambda = lambda.grid)
  
  #visualize coefficient shrinkage
  plot(lasso.models, xvar = "lambda", label = TRUE, main = paste("Lasso Regression:", i))
  
  #Cross Validation to find best lambda
  set.seed(0)
  cv.lasso.models <- cv.glmnet(X.train, y.train, alpha = 1, lambda = lambda.grid, nfolds = 10)
  
  #visualize cross validation for lambda that minimizes the mean squared error.
  plot(cv.lasso.models, main = paste("Lasso Regression:", i))
  
  #Checking the best lambda
  log(cv.lasso.models$lambda.min)
  best.lambda <- cv.lasso.models$lambda.min
  print(paste(i, ' best.lambda:', best.lambda))
  # best lambda with all the variables was found to be 0.0006892612
  # best lambda with only the bwdBIC coefficients included was found to be 0.0003053856
  
  #looking at the lasso coefficients for the best.lambda
  best.lambda.coeff <- predict(lasso.models, s = best.lambda, type = "coefficients")
  print(best.lambda.coeff)
  
  #fitting a model with the best lambda found to be 0.000689 and using it to make predictions for the testing data.
  lasso.best.lambda.train.pred <- predict(lasso.models, s = best.lambda, newx = X.test)
  lasso.best.lambda.train.pred
  
  #checking MSE
  MSE.lasso <- mean((lasso.best.lambda.train.pred - y.test)^2)
  sat.data.split <- test_train_split(xy.sat.splits[[i]], Avg.bc ~ .)
  sat.model.bc <- lm(Avg.bc ~., data = as.data.frame(cbind(sat.data.split[['X.train']], sat.data.split[['y.train']])))
  MSE.sat <- calc_MSE(sat.model.bc, as.data.frame(sat.data.split[['X.test']]), sat.data.split[['y.test']])
  
  print(paste(i, ' Lasso MSE: ', MSE.lasso, ' Saturated MSE: ', MSE.sat))
}
[1] "income  best.lambda: 0.000359381366380463"
42 x 1 sparse Matrix of class "dgCMatrix"
                                                                                                         s1
(Intercept)                                                                                   -17.284028557
Year                                                                                            0.013476737
NameAlternative_Fuels_and_Electric_Vehicle_Recharging_Property_Credit                          -1.311613095
NameAlternative_Minimum_Tax_Credit                                                             -2.231733278
NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___On_or_after_6_23_08_but_before_7_1_15   1.563930684
NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___On_or_after_7_1_15                      2.495348478
NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___Prior_to_6_23_08                        1.252395863
NameClean_Heating_Fuel_Credit                                                                  -3.196327520
NameConservation_Easement_Tax_Credit                                                           -2.276656433
NameCredit_for_Employment_of_Persons_with_Disabilities                                         -3.290414339
NameCredit_for_Purchase_of_an_Automated_External_Defibrillator                                 -3.159453144
NameEmpire_State_Apprentice_Tax_Credit                                                         -3.376054527
NameEmpire_State_Film_Post_Production_Credit                                                    0.932428124
NameEmpire_State_Film_Production_Credit                                                         2.721680583
NameEZ_QEZE_Tax_Credits___EZ_Investment_Tax_Credit                                              0.574494696
NameEZ_QEZE_Tax_Credits___QEZE_Credit_for_Real_Property_Taxes                                   0.960915301
NameEZ_QEZE_Tax_Credits___QEZE_Tax_Reduction_Credit                                            -1.075189828
NameEZ_QEZE_Tax_Credits___QEZE_Tax_Reduction_Credit_For_Corporate_Partners                     -1.501009194
NameFarm_Workforce_Retention_Credit                                                            -1.861878308
NameFarmers__School_Tax_Credit                                                                 -1.462208940
NameHire_a_Veteran_Credit                                                                      -3.075132150
NameHistoric_Properties_Rehabilitation_Credit                                                   1.795906161
NameIndustrial_or_Manufacturing_Business_Tax_Credit                                            -1.970508839
NameLong_Term_Care_Insurance_Credit                                                            -2.991508779
NameLow_Income_Housing_Credit                                                                  -1.276270928
NameManufactureru0092s_Real_Property_Tax_Credit                                                -1.538480115
NameManufacturer_s_Real_Property_Tax_Credit                                                    -1.815450711
NameMinimum_Wage_Reimbursement_Credit                                                          -1.376381572
NameMortgage_Servicing_Tax_Credit                                                              -0.965444029
NameNew_York_Youth_Jobs_Program_Tax_Credit                                                     -1.590640664
NameQETC_Employment_Credit                                                                     -0.853986295
NameSpecial_Additional_Mortgage_Recording_Tax_Credit                                           -0.372417089
NameSTART_UP_NY_Tax_Elimination_Credit                                                         -2.300657711
Group1_000_000___24_999_999                                                                     1.151959932
Group100_000___499_999                                                                          0.353836083
Group100_000_000___499_999_999                                                                  1.726777151
Group25_000_000___49_999_999                                                                    1.377240385
Group50_000_000___99_999_999                                                                    1.526670338
Group500_000___999_999                                                                          0.591982587
Group500_000_000___and_over                                                                     2.412492613
GroupZero_or_Net_Loss                                                                           1.042816832
Num                                                                                            -0.001613791
[1] "income  Lasso MSE:  1.45647173028653  Saturated MSE:  1.47368550172763"

[1] "industry  best.lambda: 0.000114975699539774"
43 x 1 sparse Matrix of class "dgCMatrix"
                                                                                                        s1
(Intercept)                                                                                   -61.87390882
NameAlternative_Minimum_Tax_Credit                                                             -3.17738814
NameLong_Term_Care_Insurance_Credit                                                            -2.61687663
NameClean_Heating_Fuel_Credit                                                                  -3.20715109
NameEmpire_State_Film_Production_Credit                                                         2.50121671
NameCredit_for_Purchase_of_an_Automated_External_Defibrillator                                 -2.32395331
NameSTART_UP_NY_Tax_Elimination_Credit                                                         -2.73114539
NameMinimum_Wage_Reimbursement_Credit                                                          -1.67875085
NameEZ_QEZE_Tax_Credits___QEZE_Credit_for_Real_Property_Taxes                                   0.91834251
NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___On_or_after_6_23_08_but_before_7_1_15   1.63074712
NameHistoric_Properties_Rehabilitation_Credit                                                   1.70377612
NameExcelsior_Jobs_Program_Credit                                                               0.98122860
NameConservation_Easement_Tax_Credit                                                           -1.84268727
NameCredit_for_Employment_of_Persons_with_Disabilities                                         -2.02070562
NameFarmers__School_Tax_Credit                                                                 -1.76586266
NameEZ_QEZE_Tax_Credits___EZ_Investment_Tax_Credit                                              0.54112912
NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___Prior_to_6_23_08                        0.78546985
NameManufactureru0092s_Real_Property_Tax_Credit                                                -1.32671371
NameBrownfield_Tax_Credits___Redevelopment_Tax_Credit___On_or_after_7_1_15                      2.14607941
`GroupOther_Services_(except_Public_Administration)`                                           -0.39320233
NameEmpire_State_Film_Post_Production_Credit                                                    0.73195196
GroupManagement_of_Companies_and_Enterprises                                                    0.47699822
NameFarm_Workforce_Retention_Credit                                                            -1.68344698
NameManufacturer_s_Real_Property_Tax_Credit                                                    -1.55252782
NameQETC_Employment_Credit                                                                     -1.06268465
NameEZ_QEZE_Tax_Credits___QEZE_Tax_Reduction_Credit_For_Corporate_Partners                     -1.31500410
Year                                                                                            0.03534486
NameNew_York_Youth_Jobs_Program_Tax_Credit                                                     -0.75302790
NameEZ_QEZE_Tax_Credits___QEZE_Tax_Reduction_Credit                                            -0.63972813
GroupAgriculture__Forestry__Fishing_and_Hunting                                                -0.34353275
GroupConstruction                                                                              -0.29738810
GroupHealth_Care_and_Social_Assistance                                                         -0.29780385
NameHire_a_Veteran_Credit                                                                      -1.74532218
GroupInformation                                                                                0.47997729
NameInvestment_Tax_Credit_for_the_Financial_Services_Industry                                   0.77828597
GroupFinance_and_Insurance                                                                      0.33842083
GroupUtilities                                                                                  0.48589130
NameEmpire_State_Apprentice_Tax_Credit                                                         -2.52886106
NameAlternative_Fuels_and_Electric_Vehicle_Recharging_Property_Credit                          -0.62586141
GroupManufacturing                                                                              0.29977977
GroupProfessional__Scientific__and_Technical_Services                                           0.27403574
GroupArts__Entertainment__and_Recreation                                                        0.36963834
GroupWholesale_Trade                                                                            0.23629280
[1] "industry  Lasso MSE:  0.787120640328352  Saturated MSE:  0.757030931332998"

as.data.frame(lasso.best.lambda.train.pred) %>% mutate(Avg_in_dollars = (lasso.best.lambda.train.pred*lambda.bc+1)^(1/lambda.bc))
calc_MSE(sat.model.bc, as.data.frame(income.sat.data.split[['X.test']]), income.sat.data.split[['y.test']])
[1] 1.473686
---
title: "R Notebook"
output: html_notebook
---
Call Libraries
```{r} 
library(tidyverse)
library(caret)
library(MASS)
library(car)
library(moments)
```


Calling the Transformed Datasets
```{r}
income_cleaned = read_csv('NYS_Corp_Tax_Credit_data/income_cleaned.csv')
income_cleaned
industry_cleaned = read_csv('NYS_Corp_Tax_Credit_data/industry_cleaned.csv')
industry_cleaned
```


Creating the Models
```{r}
sat.model.summary <- function (df, field, sat.formula){
    
    #Shapiro-Wilks test to evaluate normality
    print(shapiro.test(df[[field]]))
    
    #Kurtosis evaluation (normal distribution has a value close to 3)
    print('kurtosis')
    print(kurtosis(df[[field]]))
    linear.model.cleaned = lm(sat.formula, data = df)
    print(summary(linear.model.cleaned))
    plot(linear.model.cleaned)
    
    #histograms of response variable to check distribution
    print(df %>% 
      ggplot(aes_string(field)) + 
      geom_histogram() + 
      labs(title = 'Average Credit Amount Distribution') + 
      theme(plot.title = element_text(hjust = 0.5)))
    
    #Checking multicollinearity using VIF measurement
    print(vif(linear.model.cleaned))
    influencePlot(linear.model.cleaned)
    #avPlots(linear.model.cleaned)
}


sat.formula <- Avg ~ . - Amount
sat.field <- 'Avg'

sat.model.summary(income_cleaned, sat.field, sat.formula)
income.model <- lm(sat.formula, data = income_cleaned)

sat.model.summary(industry_cleaned, sat.field, sat.formula)
industry.model <- lm(sat.formula, data = industry_cleaned)
```

Correcting violation of Normality in previous model with BoxCox transform
```{r}
bc_func <- function (lm.cleaned, lambda.range){
  bc = boxCox(lm.cleaned, lambda = lambda.range)
  #Extracting the best lambda value.
  return(bc$x[which(bc$y == max(bc$y))])
}
  
#Income Group Dataset
income.lambda.bc = bc_func(income.model, seq(-0.2, 0.2, 1/10))
income.lambda.bc

#Industry Group Dataset
industry.lambda.bc = bc_func(industry.model, seq(-0.2, 0.2, 1/10))
industry.lambda.bc

bc_transform <- function(df, lambda.bc){
  return (df %>% 
            mutate(Avg.bc = (Avg^lambda.bc -1)/lambda.bc) %>% 
            select(-c(Avg, Amount)))
}

#Income Group Dataset
income_cleaned_bc <- bc_transform(income_cleaned, income.lambda.bc)
income.model.bc = lm(Avg.bc ~ ., data = income_cleaned_bc)

#Industry Group Dataset
industry_cleaned_bc <- bc_transform(industry_cleaned, industry.lambda.bc)
industry.model.bc = lm(Avg.bc ~ ., data = industry_cleaned_bc)
```

Checking linear regression assumptions for the transformed data.
```{r}
sat.formula.bc <- Avg.bc ~ .
sat.field.bc <- 'Avg.bc'

#Income
sat.model.summary(income_cleaned_bc, sat.field.bc, sat.formula.bc)

#Industry
sat.model.summary(industry_cleaned_bc, sat.field.bc, sat.formula.bc)
```

BIC comparison before and after BoxCox transform
```{r}
BIC(income.model.bc, income.model)
BIC(industry.model.bc, industry.model)
```

Stepwise Regression on Income_cat_bc (boxcox transformed dataset)
```{r}
#creating dummy variable columns for stepwise
dummy_func <- function (df){
  x = model.matrix(Avg.bc ~., df)[, -1]
  dummy_bc = as.data.frame(x) %>% mutate(Avg.bc = df$Avg.bc)
  colnames(dummy_bc) <- str_replace_all(colnames(dummy_bc), "-|'|/| |,|�|&" , '_')
  return(dummy_bc)
}
```

Cleaning column names further so stepwise regression doesn't present any errors
```{r}
#Income Group Dataset
income.dummy.bc <- dummy_func(income_cleaned_bc)
#colnames(income.dummy.bc)[37] <- 'NameManufactureru0092s_Real_Property_Tax_Credit'
colnames(income.dummy.bc)

#Industry Group Dataset
industry.dummy.bc <- dummy_func(industry_cleaned_bc)
#colnames(industry.dummy.bc)[35] <- 'NameManufactureru0092s_Real_Property_Tax_Credit'
colnames(industry.dummy.bc)
```

Stepwise regression using BIC as the criteria (the penalty k = log(n)).
```{r}
#Creating Stepwise Models
bcs = list(income = income.dummy.bc, industry = industry.dummy.bc)
model.fulls = list(income = lm(Avg.bc ~ ., data = income.dummy.bc), industry = lm(Avg.bc ~ ., data = industry.dummy.bc)) #All variables
model.emptys = list(income = lm(Avg.bc ~ 1, data = income.dummy.bc), industry = lm(Avg.bc ~ 1, data = industry.dummy.bc)) #intercept only
k = c('income', 'industry')
forwardBIC = list(income = NULL, industry = NULL)
backwardBIC = list(income = NULL, industry = NULL)

for (i in k){
  bc = bcs[[i]]
  scope = list(lower = formula(model.emptys[[i]]), upper = formula(model.fulls[[i]]))
  n_obs = bc %>% count() %>% dplyr::first()
  forwardBIC[[i]] = step(model.emptys[[i]], scope, direction = "forward", k = log(n_obs))
  backwardBIC[[i]] = step(model.fulls[[i]], scope, direction = "backward", k = log(n_obs))
}
```

Selecting Best Formula per Dataset from Stepwise Regressions
```{r}
bic_func <- function (BIC.model, sat.model){
  print('Adjusted R Squared:')
  print(summary(BIC.model)$adj.r.squared)
  print('Number of Coefficients:')
  print(dim(summary(BIC.model)$coefficient)[1])
  print('VIF Check: ')
  print(max(vif(BIC.model)))
  print('Anova test p-value (between saturated model and stepwise):')
  print(anova(BIC.model, sat.model)$`Pr(>F)`[2])
  print("*************************")
}

a = anova(forwardBIC[['income']], model.fulls[['income']])

a$`Pr(>F)`[2]

bic_func(forwardBIC[['income']], model.fulls[['income']])
bic_func(backwardBIC[['income']], model.fulls[['income']])
bic_func(forwardBIC[['industry']], model.fulls[['industry']])
bic_func(backwardBIC[['industry']], model.fulls[['industry']])

bic_func(model.fulls[['industry']], model.fulls[['industry']])


VIF.variables <- as.data.frame(vif(model.fulls[['industry']])) %>% 
  select(VIF = `vif(model.fulls[["industry"]])`) %>% 
  filter(VIF > 5) %>% rownames()

industry.dummy.bc %>% select(-all_of(VIF.variables))

```


```{r}
#anova(model2, model.saturated)

#Income Group Dataset
income.best.formula <- backwardBIC[['income']]$call[[2]]
income.best.formula

#Industry Group Dataset
industry.best.formula <- forwardBIC[['industry']]$call[[2]]
industry.best.formula
```

Stepwise regression using BIC as the criteria (the penalty k = log(n)).
```{r}
# #Forward BIC stepwise
# forwardBIC = step(model.empty, scope, direction = "forward", k = log(n_obs))
# fwd.BIC.summary.ENI <- data.frame(summary(forwardBIC)$coefficients)
# fwd.BIC.summary.ENI %>% arrange(rownames(fwd.BIC.summary.ENI))
# 
# #Backward BIC stepwise
# backwardBIC = step(model.full, scope, direction = "backward", k = log(n_obs))
# bwd.BIC.summary.ENI <- data.frame(summary(backwardBIC)$coefficients)
# bwd.BIC.summary.ENI %>% arrange(rownames(bwd.BIC.summary.ENI))
# 
# summary(forwardBIC)
# summary(backwardBIC)
# 
# #inputing forwardBIC into a dataframe with index created as a column
# fwd.BIC.summary.ENI$ENI = rownames(fwd.BIC.summary.ENI)
# rownames(fwd.BIC.summary.ENI) = NULL
# fwd.BIC.summary.ENI
# 
# #inputing backwardBIC into a dataframe with index created as a column
# bwd.BIC.summary.ENI$ENI = rownames(bwd.BIC.summary.ENI)
# rownames(bwd.BIC.summary.ENI) = NULL
# bwd.BIC.summary.ENI
# 
# #comparing the forward and backward stepwise regression coefficients
# anti_join(fwd.BIC.summary.ENI, bwd.BIC.summary.ENI, by = 'ENI')
# inner_join(fwd.BIC.summary.ENI, bwd.BIC.summary.ENI, by = 'ENI')
# 
# #choosing backwardBIC because of negligible reduction in adjusted R^2 but we can reduce our sizable number of predictor variables.
# 
# #checking our selected model's predictor variable's VIFs
# vif(backwardBIC)
# 
# best.formula <- backwardBIC$call[[2]]
```


Splitting data up into test data and training data (test data is for year 2019, training is the rest)
```{r}
test_train_split <- function(dummy_bc, best.formula) {
  data.test <- dummy_bc %>% filter(Year == 2019)
  data.train <- dummy_bc %>% filter(Year != 2019)
  
  #train
  #X.train <- as.matrix(data.train %>% select(-Avg.bc))
  X.train <- model.matrix(best.formula, data = data.train)[,-1]
  y.train <- as.matrix(data.train %>% select(Avg.bc))

  #test
  #X.test <- as.matrix(data.test %>% select(-Avg.bc))
  X.test <- model.matrix(best.formula, data = data.test)[,-1]
  y.test <- as.matrix(data.test %>% select(Avg.bc))
  return (list('X.train' = X.train, 'y.train' = y.train, 'X.test' = X.test, 'y.test' = y.test))
}


income.data.split <- test_train_split(income.dummy.bc, income.best.formula)
income.data.split[['y.train']]

industry.data.split <- test_train_split(industry.dummy.bc, industry.best.formula)

# data.test <- dummy_bc %>% filter(Year == 2019)
# data.train <- dummy_bc %>% filter(Year != 2019)
# 
# #training model based on best.formula from stepwise
# train.model <- lm(best.formula, data = data.train)
# summary(train.model)
# 
# #train
# #X.train <- as.matrix(data.train %>% select(-Avg.bc))
# X.train <- model.matrix(best.formula, data = data.train)[,-1]
# y.train <- as.matrix(data.train %>% select(Avg.bc))
# 
# #test
# #X.test <- as.matrix(data.test %>% select(-Avg.bc))
# X.test <- model.matrix(best.formula, data = data.test)[,-1]
# y.test <- as.matrix(data.test %>% select(Avg.bc))
# 
# dim(X.train)
# dim(X.test)
```


Lasso regression for comparison to backward stepwise
```{r}
calc_MSE <- function (model, x.test, y.test){
  y.predict <- predict(model, newdata = x.test)
  return(mean((y.predict - y.test)^2))
}

xy.sat.splits <- list('income' = income.dummy.bc, 'industry' = industry.dummy.bc)
xy.splits <- list('income' = income.data.split, 'industry' = industry.data.split)

for (i in k){
  X.train <- xy.splits[[i]][['X.train']]
  y.train <- xy.splits[[i]][['y.train']]
  X.test <- xy.splits[[i]][['X.test']]
  y.test <- xy.splits[[i]][['y.test']]
  
  #create lambda grid
  lambda.grid = 10^seq(2, -5, length = 100)
  
  #create lasso models with lambda.grid
  lasso.models = glmnet(X.train, y.train, alpha = 1, lambda = lambda.grid)
  
  #visualize coefficient shrinkage
  plot(lasso.models, xvar = "lambda", label = TRUE, main = paste("Lasso Regression:", i))
  
  #Cross Validation to find best lambda
  set.seed(0)
  cv.lasso.models <- cv.glmnet(X.train, y.train, alpha = 1, lambda = lambda.grid, nfolds = 10)
  
  #visualize cross validation for lambda that minimizes the mean squared error.
  plot(cv.lasso.models, main = paste("Lasso Regression:", i))
  
  #Checking the best lambda
  log(cv.lasso.models$lambda.min)
  best.lambda <- cv.lasso.models$lambda.min
  print(paste(i, ' best.lambda:', best.lambda))
  # best lambda with all the variables was found to be 0.0006892612
  # best lambda with only the bwdBIC coefficients included was found to be 0.0003053856
  
  #looking at the lasso coefficients for the best.lambda
  best.lambda.coeff <- predict(lasso.models, s = best.lambda, type = "coefficients")
  print(best.lambda.coeff)
  
  #fitting a model with the best lambda found to be 0.000689 and using it to make predictions for the testing data.
  lasso.best.lambda.train.pred <- predict(lasso.models, s = best.lambda, newx = X.test)
  lasso.best.lambda.train.pred
  
  #checking MSE
  MSE.lasso <- mean((lasso.best.lambda.train.pred - y.test)^2)
  sat.data.split <- test_train_split(xy.sat.splits[[i]], Avg.bc ~ .)
  sat.model.bc <- lm(Avg.bc ~., data = as.data.frame(cbind(sat.data.split[['X.train']], sat.data.split[['y.train']])))
  MSE.sat <- calc_MSE(sat.model.bc, as.data.frame(sat.data.split[['X.test']]), sat.data.split[['y.test']])
  
  print(paste(i, ' Lasso MSE: ', MSE.lasso, ' Saturated MSE: ', MSE.sat))
}

```

```{r}
as.data.frame(lasso.best.lambda.train.pred) %>% mutate(Avg_in_dollars = (lasso.best.lambda.train.pred*lambda.bc+1)^(1/lambda.bc))
```

```{r}
income.sat.data.split <- test_train_split(income.dummy.bc, Avg.bc ~ .)
income.sat.data.split[['X.train']]

sat.model.bc <- lm(Avg.bc ~., data = as.data.frame(cbind(income.sat.data.split[['X.train']], income.sat.data.split[['y.train']])))
summary(sat.model.bc)

calc_MSE(sat.model.bc, as.data.frame(income.sat.data.split[['X.test']]), income.sat.data.split[['y.test']])


sat.y.predict <- predict(sat.model.bc, newdata = as.data.frame(income.sat.data.split[['X.test']]))
mean((sat.y.predict - income.sat.data.split[['y.test']])^2)
```

